Hypergeometric expressions of $L$-values for a Borweins theta product of weight $3$

Abstract

In this paper, we consider a modular form of weight 3, which is a product of the Borweins theta series, and express its L-values at s = 1, 2 and 3 in terms of special values of Kampé de Fériet hypergeometric functions, which are two-variable generalization of generalized hypergeometric functions.